These lecture notes have been written for courses given at École normale supérieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general introduction to the foundations of code-based cryptography which is currently known to be secure even against quantum adversaries. In particular we focus our attention to the decoding problem whose hardness is at the ground of the security of many cryptographic primitives, the most prominent being McEliece and Alekhnovich' encryption schemes.